if cos 20 - sin 20=p, find the value of cos 40 in terms of p

DEar Beverly

cos 20 - sin 20=p

square it

cos²20 + sin²20 -2sin20cos20 =p²

sin40 =1-p²

and cos40 =(1-sin²40)^1/2

                   =(2p²-p⁴)^1/2

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